Exact integer spectra of a constrained leakage commutator: a marked-occupancy transfer construction

This record contains the manuscript and verification scripts for “Exact integer spectra of a constrained leakage commutator: a marked-occupancy transfer construction.” Projection can turn a commuting pair of operators into a non-commuting pair after compression to a constrained Hilbert space. For a periodic two-leg hard-core ladder with leg-resolved spin-flip moves, the manuscript solves the resulting commutator spectrum exactly. A marked occupancy partition function returns both the constrained state count and the complete spectral generating function. An occupancy-block decomposition proves the full integer spectrum and all multiplicities for every ladder length L ≥ 3 , the Pell–Lucas trace law, and the normalized thermodynamic spectral limit. Files included: main_paper1_rv1.4_1.pdf — submission-ready manuscript. paper1_spectrum_checks.py — constructs the constrained basis, projected drives, and leakage commutator, and reproduces the finite-size spectral and trace checks. paper1_occupancy_transfer_checks.py — verifies the occupancy census, block multiplicities, characteristic-polynomial exponents, trace law, and marked transfer identity. paper1_lie_closure_lower_bounds.py — reproduces the finite-field lower bounds for the Lie algebra generated by the projected drives. The all-L spectral results are proved analytically in the manuscript. The Python scripts provide independent finite-size verification and reproducibility checks.